CBSE Class 12 Mathematics Inverse Trigonometric Functions MCQs Set 02

Question. if 3 sin^-1 2x/1+x² -4cos^-1 1-x²/1+x² + 2 tan^-1 2x/1-x² = π/3, then value of x is
(a) √3
(b) 1/√3
(c) 1
(d) None of the options

Answer : B

Question. The sum of the infinite series cot ^-1 2+cot^-1 8+cot^-1 18+ cot^-1
(a) π
(b) π/2
(c) π/4
(d) None of the options

Answer : C

Question. The value of cos ( 2cos^-1 x+ sin^-1x) at x =1/5 is
(a) 1
(b) 3
(c) 0
(d) -2√6/5

Answer : D

Question. If tan-1(a/x)+ tan-1(b/x)=π/2,then x is equal to
(a) √ab
(b) √2ab
(c) 2ab
(d) ab

Answer : A

Question. The value of the expression tan(1/2 cos ^-1 2/√5)  is
(a) 2 √5
(b) √5-2
(c) √5+2
(d) 5+√2

Answer : B

Question. If in a Δ ABC, ∠A = tan ^-12 and ∠B = tan -13, then ∠C is equal to
(a) π/2
(b) π/3
(c) π/4
(d) None of the options

Answer : C

Question. If 2 tan^-1 (cos x) = tan^-1 (2cosec x), then the value of x is
(a) 3π/4
(b) π/4
(c) π/3
(d) None of the options

Answer : B

Question. If tan^–1 x + tan^–1 y = 4π/5, then cot^–1 x + cot^–1 y equals
(a) π/5
(b) 2π/5
(c) 3π/5
(d) p

Answer : A

Question. The principle value of the expression cos^–1[cos(–680°)] is
(a) 2π/9
(b) − 2π/9
(c) 34π/9
(d) π/9

Answer : A

Question. If tan^-1(x-1/x+2)+ tan^-1 (x+1/x+2)=π/4, then x is equal to
(a) 1/√2
(b) -1/√2
(c) ±√5/2
(d) ±1/2

Answer : C

Question. If co^-1 x+cos^-1 y + cos^-1 z= π, then
(a) x2 + y2 = z2
(b) x2 + y2 + z2 = 0
(c) x2 + y2 + z2 = 1-2xyz
(d) None of the options

Answer : C

Question. 4 tan ^-1 1/5- tan ^-1 1/239 is equal to
(a) π
(b) π/2
(c) π/3
(d) π/4

Answer : D

Question. If tan θ +tan (π/3+θ) +tan (-π/3+θ )=a tan 3θ,then a   is equal to
(a) 1/3
(b) 1
(c) 3
(d) None of the options

Answer : C

Question. The value of cot^-1(xy+1/x-y) +cot^-1(yz+1/y-z)+cot^-1(zx+1/z-x)  is
(a) 0
(b) 1
(c) cot-1 x+cot-1y +cot-1 z
(d) None of the options

Answer : A

Question. The value of the expression sin(2 tan^-1 1/3) + cos (tan-1 2√2) 
a) 13/15
(b) 14/15
(c) 11/15
(d) None of the options

Answer : B

Case Based Questions

Question. The value of sin [cos^-1(7/25)] is
(a) 25/24
(b) 25/7
(c) 24/25
(d) 7/24

Answer : C

Question. sin^-1(−1/2)
(a) π/3
(b) –π/3
(c) π/6
(d) –π/6

Answer : D

Question. cosec^-1(−2/√3)
(a) π/6
(b) π/3
(c) 5π/6
(d) –2π/3

Answer : C

Question. cosec^-1(−2/√3)
(a) –π/3
(b) π/3
(c) π/2
(d) –π/2

Answer : A

Question. If 3 tan^-1 x + cot^-1 x = π, then x equals
(a) 0
(b) 1
(c) -1
(d) 12

Answer : B

Question. The value of cos^-1[cos(33π/5)] is
(a) 3π/5
(b) −3π/5
(c) π/10
(d) –π/10

Answer : A

Question. The domain of the function cos^-1 (2x – 1) is
(a) [0, 1]
(b) [-1, 1]
(c) [-1, -1]
(d) [0, π]

Answer : A

Question. If cos(sin^-12/5 + cos^-1 x) = 0 then x is equal to
(a) 1/5
(b) 2/5
(c) 0
(d) 1

Answer : B

Question. Maximum value of f(x)
(a) [–1, 1]
(b) [0, ∞)
(c) (–∞, 0]
(d) not maxima

Answer : D

Question. Which of the following is the principal value branch of cosec^-1 x?
(a) (−π/2, π/2)
(b) (0, π) – {π/2}
(c) [−π/2, π/2]
(d) [−π/2, π/2] – [0]

Answer : D

Question. The value of sin (2 tan^-1 (0.75)) is equal to
(a) 0.75
(b) 1.5
(c) 0.96
(d) sin (1.5)

Answer : C

Question. The value of cos^-1 (cos3π/2) is equal to
(a) π/2
(b) 3π/2
(c) 5π/2
(d) –7π/2

Answer : A

Question. The value of expression 2 sec^-1 (2) + sin^-1 (1/2) is
(a) π/6
(b) 5π/6
(c) 7π/6
(d) 1

Answer : B

Question. If sin-1(2a/1+a²) + cos^-1(1−a²/1+a²) = tan-1(2x/1−x²) where a, x ∈ |0, 1| then the value of x is
(a) 0
(b) a2
(c) a
(d) 2a/1−a2

Answer : D

Question. cot^-1(1)
(a) π/3
(b) π/4
(c) π/2
(d) 0

Answer : B

Question. cos^-1(√3/2)
(a) 5π/6
(b) π/6
(c) 4π/9
(d) 2π/3

Answer : A

Question. cosec^-1(2)
(a) π/6
(b) 2π/3
(c) 5π/6
(d) 0

Answer : A

Question. sec^-1(2)
(a) π/6
(b) π/3
(c) 2π/3
(d) 5π/6

Answer : B

Question. tan^-1(√3)
(a) π/6
(b) π/3
(c) 2π/3
(d) 5π/6

Answer : B

Question. cot^-1(-√3)
(a) 5π/6
(b) π/3
(c) π/2
(d) π/4

Answer : A

Question. tan-1 (√3) + sec^-1 (-2) – cosec^-1(2/√3)
(a) 5π/6
(b) 2π/3
(c) π/3
(d) 0

Answer : D

Question. cos^-1 (−1/2) + 2sin^-1 (−1/2)
(a) π/3
(b) 2π/3
(c) 3π/4
(d) 5π/8

Answer : A